Which is the equation of an ellipse with directrices at x = ±4 and foci at (2, 0) and (−2, 0)? x squared over 8 plus y squared over 4 equals 1
x squared over 16 plus y squared over 4 equals 1
x squared over 8 minus y squared over 4 equals 1
x squared over 16 minus y squared over 4 equals 1

x squared over 8 plus y squared over 4 equals 1

Step-by-step explanation:

The general equation of ellipse is given by :-

For foci =(c,0) , and a>b we have  .

Given, For an ellipse , we have

Directrix at x = ±4 and foci at (2, 0) and (−2, 0).

Since, directrix = and , where e is the eccentricity.

That means

Also,

So, the equation of ellipse becomes

hence, the correct option is .

except a rational number. : )